IT-CESENATICO 1998 Problem 4

Let $ABCD$ be a trapezoid with the longer base $AB$ such that its diagonals $AC$ and $BD$ are perpendicular. Let $O$ be the circumcenter of the triangle $ABC$ and $E$ be the intersection of the lines $OB$ and $CD$ . Prove that $BC^2 = CD \cdot CE$ .